In Takeout Town, there are 70 identical pizza delivery firms, each firm having t
ID: 1107074 • Letter: I
Question
In Takeout Town, there are 70 identical pizza delivery firms, each firm having the cost function
c(q) = 0.5q2 + 44q + 98
where q is the quantity of pizzas produced by a typical firm. The market demand curve is given by
Qd(p) = 820 5p.
(a) Find a firm's individual supply curve
qs(p)
and the market supply curve
Qs(p).
Calculate the market equilibrium price p* and quantity Q*.
Calculate the firm output q* and profit level.
(b) What will be the long-run price
plr
after entry or exit?
plr = $
Calculate the approximate number of firms in the long run (round down to the nearest integer).
pizza delivery firms
Explanation / Answer
c(q) = 0.5q2 + 44q + 98
Qd(p) = 820 5p
(a)
(i) Individual supply function is the Marginal cost (MC) function.
MC = dc(q) / dq = q + 44
Individual supply function:
MC = p = q + 44
q = p - 44
(ii) Since there are 70 firms,
Market supply (Qs) = 70 x q
q = Qs / 70
Substituting in individual supply function,
Qs / 70 = p - 44
Qs = 70p - 3,080 [Market supply]
(iii) In equilibrium, Qd = Qs
820 - 5p = 70p - 3,080
75p = 3,900
p = 52
Q = 820 - (5 x 52) = 820 - 260 = 560
p* = 52
Q* = 560
q* = Q* / 70 = 560 / 70 = 8
Profit = Revenue - Cost = (p* x q*) - c(q) = (52 x 8) - [(0.5 x 8 x 8) + (44 x 8) + 98]
= 416 - (32 + 352 + 98) = 416 - 482
= - 66 (Loss)
(b) Short run loss will lead to exit, and in long run equilibrium, p = AC = MC
AC = c(q) / q = 0.5q + 44 + (98 / q)
MC = q + 44
Equating MC and AC,
q + 44 = 0.5q + 44 + (98 / q)
0.5q = 98 / q
q2 = 196
q = 14
When q = 14, MC = q + 44 = 58
Price = MC = 58
When p = 58, Qd = 820 - (5 x 58) = 820 - 290 = 530
Number of firms = Qd / q = 530 / 14 = 37.86 ~ 37 (Rounded down to nearest integer)
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